MinT - Best Known (68−37, 68, s)-Nets in Base 25

Best Known (68−37, 68, s)-Nets in Base 25

(68−37, 68, 204)-Net over F₂₅ — Constructive and digital

Digital (31, 68, 204)-net over F₂₅, using

t-expansion [i] based on digital (30, 68, 204)-net over F₂₅, using
- net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
    - a function field by GarcÃa and Quoos [i]

(68−37, 68, 261)-Net over F₂₅ — Digital

Digital (31, 68, 261)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(68−37, 68, 50266)-Net in Base 25 — Upper bound on s

There is no (31, 68, 50267)-net in base 25, because

1 times m-reduction [i] would yield (31, 67, 50267)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 4591 906710 588100 763932 410469 747625 823902 482889 406604 147366 172069 395108 979868 714100 517350 596625 > 25⁶⁷ [i]